Question: Simplify the following expression: $ q = \dfrac{-9z - 3}{-5z - 4} + \dfrac{10}{7} $
Solution: In order to add expressions, they must have a common denominator. Multiply the first expression by $\dfrac{7}{7}$ $ \dfrac{-9z - 3}{-5z - 4} \times \dfrac{7}{7} = \dfrac{-63z - 21}{-35z - 28} $ Multiply the second expression by $\dfrac{-5z - 4}{-5z - 4}$ $ \dfrac{10}{7} \times \dfrac{-5z - 4}{-5z - 4} = \dfrac{-50z - 40}{-35z - 28} $ Therefore $ q = \dfrac{-63z - 21}{-35z - 28} + \dfrac{-50z - 40}{-35z - 28} $ Now the expressions have the same denominator we can simply add the numerators: $q = \dfrac{-63z - 21 - 50z - 40}{-35z - 28} $ $q = \dfrac{-113z - 61}{-35z - 28}$ Simplify the expression by dividing the numerator and denominator by -1: $q = \dfrac{113z + 61}{35z + 28}$